在$L^1$空间上, 研究了种群细胞增生中一类具扰动项的一般边界条件下的L-R模型, 利用有关半群和扰动定理等现代分析方法, 证明了这类模型相应的迁移算子生成正不可约$C_0$半群, 讨论了该迁移算子的谱分析, 获得了该模型相应的迁移方程解在一致拓扑意义下的渐近行为等结果.

This paper is to research the L-R model with perturbation term of cell populations with generalized boundary condition in $L^1$ space, by using the modern analysis method of the relative semigroup and perturbation theorem, It is proved that the irreducibility of the positive $C_0$ semigroup generated by the transport operator corresponding for this model, and it is to obtain that the asymptotic behavior of the transport equation's solution in the uniform topology, and so on.